This is surprisingly subtle.
When, for instance, when bank A in the Richmond Federal Reserve district sends $1000 in reserves to bank B in the Minneapolis Federal Reserve district, reserves are taken out of bank A's account at the Richmond Fed and placed into bank B's account at the Minneapolis Fed.
Now, bank A's reserves are a liability on the books of the Richmond Fed, while bank B's reserves are a liability on the books of the Minneapolis Fed. Without any offsetting change, therefore, the process would result in the Richmond Fed discharging a liability and the Minneapolis Fed gaining a liability - and if this continued, regional Fed assets and liabilities could become highly mismatched.
The principle, then, is that there should be an offsetting swap of assets. It would be too complicated to swap actual assets every time there is a flow of reserves between banks in different districts. (There's over $3 trillion in transactions every day on Fedwire, the Fed's RTGS system - and if even a fraction of those are between different districts, the amounts are really enormous.) Instead, in the short run the regional Feds swap accounting entries in an "Interdistrict Settlement Account" (ISA). In the example above, the Minneapolis Fed's ISA position would increase by \$1000, while the Richmond Fed's ISA position would decrease by \$1000, to offset the transfer of liabilities.
So far, this is all very similar to the controversial TARGET2 system in the Euro area, in which large balances between national banks have recently been accumulating. The American system is different, however, because ISA entries are eventually settled via transfers of assets. Every April, the average ISA balance for each regional Fed over the past year is calculated, and this portion of the balance is settled via a transfer of assets in the System Open Market Account (the main pile of Fed assets, run by the New York Fed). Hence, if in April the Minneapolis Fed has an ISA balance of +\$500, but over the past year it had an average balance of +\$2000, its balance is decreased (by \$2000) to -\$1500, and it has an offsetting gain of \$2000 in SOMA assets.
As this example shows, since it is average balances over the past year that are settled, not the current balances, ISA balances do not necessarily go to zero every April. Historically, they were fairly tiny anyway, but since QE brought dramatic increases in reserves, these balances have sometimes been large and irregular. In the long run, though, the system prevents any persistent imbalances from accumulating.
(Note: the process in April is a little bit more complicated than I describe, since some minor transfers of gold certificate holdings are also involved. Basically, gold certificates are transferred between regional Feds to maintain a constant ratio of gold certificates to federal reserve notes; the transfers of SOMA assets are adjusted to account for this. Wolman's recent piece for the Richmond Fed is one of the few sources that describes the system in detail.)